DIYARBAKIR, Turkey (Reuters) -- Security forces killed 32 Kurdish militants in Turkey's mainly Kurdish southeast at the weekend, army and security sources said on Sunday, escalating the conflict in the region.

It was one of the bloodiest weekends since the three-decades-old Kurdish insurgency resumed last July, wrecking a peace process launched by Ankara with the jailed leader of the militant Kurdistan Workers Party (PKK) in late 2012.

Weekend media reports said Prime Minister Ahmet Davutoglu told a closed-door meeting of his ruling AK Party that security operations and curfews in the region would end within a week, but he said on Sunday there was no such timescale.

"We will pursue our anti-terror fight with great determination until...our mountains, plains and towns are cleansed of these killers," he said in a televised speech at the end of the meeting.

In the region's largest city, Diyarbakir, a soldier and a police officer were killed on Sunday when they came under explosives and rifle fire in a clash with rebels in which 14 security personnel were also wounded, security sources said.

Gunfire and blasts could be heard echoing around the heavily damaged historical district of Sur where the clash occurred.

Since the PKK launched its insurgency in 1984, fighting has been largely in the countryside, but the latest violence has focused on urban areas, where the PKK youth wing has set up barricades and dug trenches to keep security forces out.

Civilians have been caught in the middle. According to figures from the pro-Kurdish HDP party, 81 civilians have been killed in Sur and two towns near the Syrian and Iraqi borders since they were placed under 24-hour curfew last month.

Thousands of people have left their homes in the towns. Residents complain of indiscriminate operations and say the curfews have even prevented the sick from getting to hospital.

On Saturday, 16 rebels were killed in the towns of Cizre and Silopi, near the Syrian and Iraqi borders, and another four were killed in Sur, the armed forces said in a statement.

It said that a total of 448 militants had been killed in those three areas since they were placed under curfew and security operations were launched last month.

Police killed a further 12 PKK members after finding them in a house in the southeastern city of Van overnight, security sources said. One police officer died and two others were wounded in the operation.

The PKK, designated a terrorist group by Turkey, the United States and the European Union, says it is fighting for autonomy and greater rights for Kurds in the NATO member country.

More than 40,000 people have been killed in the conflict.

President Tayyip Erdogan has said 3,100 PKK members were killed in operations inside and outside Turkey in 2015. The PKK is based in camps in the mountains of northern Iraq, which have been targeted by Turkish warplanes since the conflict resumed.